Optical lenses are used to focus a beam of light. However the size of the focused spot is limited from diffraction theory. One such equation, which is discussed by E. Hecht in "Optics", (Addison-Wesley, Mass., 1988), gives the diameter d of the focused spot by the equation ##EQU1## where .lambda. is the wavelength of the light, and f is the focal length of the lens. Here D usually represents the diameter of the lens assuming that the lens is completely illuminated. Otherwise it represents the diameter of the optical beam if it is smaller than the lens. FIG. 1A shows the formation of a diffraction limited spot by a lens.
There are many applications in which a very small focused spot size is desired such as in photolithography, in making high density computer memory chips, in laser machining where high energy densities are desired, and in the reading and writing of compact discs where smaller spot sizes mean longer playing times and higher memory content. According to Eq. (1), three ways of decreasing the spot size are to use shorter wavelengths, shorter focal lengths, or larger diameters. However diffraction theory places a limit on that size.
In order to focus the light, the phase of the incident optical beam .phi.(x,y) must be altered as a function of x and y. This phase function is discussed by A. Yariv in "Introduction to Optical Electronics", (Holt, Rinehart, and Winston, N.Y., 1991) and is given, using small angle approximation theory, by ##EQU2## where f is the focal length of the lens and k=2.pi./.lambda..
More complicated aspheric phase functions are required to obtain the diffraction limited size for the focused spot size as known to those skilled in the art. Some of these are discussed by Kedmi et. al. in U.S. Pat. No. 5,073,007 titled "Diffractive optical element". Lens functions can operate either in transmission as with conventional glass lenses, or in reflection as in the case of focusing mirrors.
For purposes of this Specification, the term "lens function" is defined as a phase and/or amplitude function and which operates either in a reflection or transmission mode.
The phase shift of light traveling through a medium of thickness d is related to ##EQU3## where n is the index of refraction of the medium. This phase can be encoded by varying the index of refraction or the thickness of the material.
The phase function can be encoded to form a lens using several techniques as known to those skilled in the art. The first is refraction and involves the bending of light as it passes through an interface between two different materials such as glass and air. By making a curved glass element as shown in FIG. 1A, different rays of light will be bent by different amounts as they pass through the lens. The phase function is controlled by varying the thickness of the glass lens. By making the glass surfaces with the correct shapes, diffraction limited lenses can be manufactured. These lenses are called refractive optical elements and are the most common lenses available.
A second technique known in the prior art involves diffraction. This approach uses the well known diffraction formula m.lambda.=psin.theta. where m is the order, .lambda. is the wavelength, p is the grating spacing and .theta. is the angle from normal to the grating. If the grating spacing p varies with distance r from the axis in the correct manner as discussed by E. Hecht in "Optics", (Addison-Wesley, Mass., 1988), then the diffraction angle will vary also as shown in FIG. 1B, again forming a focused spot. These lenses are called diffractive optical elements. Examples of such lenses are Fresnel lenses, binary optical elements, and holographic optical elements.
In making Fresnel lenses, the phase function forming the diffraction grating can be encoded using a variety of techniques. A discussion of these techniques can be found in several articles in "Proceedings of SPIE", Volume 1052, (1989).
These encoding techniques can be understood using the Euler relation where .phi.(x,y) is given by Eq. (2), as EQU e.sup.i.phi.(x,y) =cos(.phi.(x,y))+i sin(.phi.(x,y)) (4)
Here the real part is given by cos(.phi.(x,y)) and the imaginary part by sin(.phi.(x,y)). The phase function can be encoded by examining the entire phase function, or only its real or imaginary part.
Some representative phase encoding techniques for making diffractive optical elements or binary optical elements include:
1. Making the grating with adjacent transparent and opaque circular regions. This pattern can be described as a zone plate with alternating transparent regions as discussed by M. V. Klein in "Optics" (J. Wiley and Sons, New York, 1970). In this approach, the phase function is made using a computer program. In one example the phase function is made equal to +1 whenever the Real part of the complex function shown in Eq. (4) is positive. When the Real part of the complex function shown in Eq. (4) is negative or zero, the phase function is made equal to 0.
2. Making the grating with adjacent regions in which the phase of the transmission differs by .pi. radians from one region to another. This pattern is referred to as a binary phase-only filter (BPOF). In this approach, the phase function is made using a computer program as discussed by D. Psaltis et. al. in "Optical image correlation with a binary spatial light modulator" published in Optical Engineering, vol 23, p 698-704, Nov/Dec. (1984). In one example whenever the Real part of the complex function shown in Eq. (4) is positive, the phase function is made equal to +1. When the Real part of the complex function shown in Eq. (4) is negative or zero, the phase function is made equal to -1.
3. Using holographic techniques to encode the phase function as discussed by M. Feldman and C. Guest in the article titled "Computer generated holographic optical elements for optical interconnection of very large scale integrated circuits" published in Applied Optics, vol 26, p 4377-4384, (1987).
4. Using photolithography or a ultraviolet laser writer combined with reactive ion etching to selectively vary the thickness of the optical element to encode the required phase function as discussed by Y. Carts in the article titled "Microelectronic methods push binary optics frontiers" published in Laser Focus World, p. 87-95, February (1992).
5. Using direct e-beam writing to selectively vary the thickness of the optical element to encode the required phase function as discussed by Y. Carts in the article titled "Microelectronic methods push binary optics frontiers" published in Laser Focus World, p. 87-95, February (1992).
6. Using diamond turning to selectively cut the surface of the optical element to encode the required phase function as discussed by Y. Carts in the article titled "Microelectronic methods push binary optics frontiers" published in Laser Focus World, p. 87-95, February (1992).
7. Using an ion exchange process to selectively vary the phase profile of a material by varying the index of refraction of the material as a function of position as discussed by H. Bolstad et. al. in the article titled "Optimization of phase-only computer generated holograms using an ion-exchange process" published in Optical Engineering, vol 31, p. 1259-1263, (1992).
8. Using replication techniques in which a master surface-engineered diffractive optical element is first produced using techniques such as discussed above. Then replica copies can be made by impressing the surface relief pattern onto another material including a variety of plastic materials as discussed by Y. Carts in the article titled "Microelectronic methods push binary optics frontiers" published in Laser Focus World, p. 87-95, February (1992).
Optical elements can also be made using a combination of refractive and diffractive techniques. This approach offers several advantages including correction of chromatic aberrations as discussed by T. Stone et. al. in the article titled "Hybrid diffractive-refractive lenses and achromats" and published in Applied Optics, vol 27, p 2960-2971, (1988).
Finally, optical elements can be made encoding the desired phase function onto programmable recording media including spatial light modulators (SLMs). Some of the devices which are well known to those in the field include the magneto-optic spatial light modulator (MOSLM), liquid crystal light valve (LCLV), liquid crystal television (LCTV), and deformable mirror device (DMD). These modulators can allow encoding of pure amplitude information, a binary phase pattern, a pure phase-only function, or combinations of amplitude and phase information. FIG. 1C shows the formation of a focused spot by diffractive optical elements which has been encoded onto a SLM.
Diffractive optical elements can offer more design freedom than refractive optical elements since the phase distribution can be varied more easily allowing the construction of more complicated optical elements.
Nevertheless, despite the longstanding goal of obtaining a subdiffraction limited focused beam, the problem remains unsolved.